The pair of linear equations 2x + 5y = –11 and 5x + 15y = –44 has: 

(a) many solutions

(b) no solution

(c) one solution

(d) 2 solutions

If a pair of linear equations is consistent, then the lines will be:

(a) always intersecting

(b) always coincident

(c) intersecting or coincident

(d) parallel

The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages in years of the son and the father

respectively are:

(a) 4 and 24

(b) 6 and 36

(c) 5 and 30

(d) 7 and 42

In the equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\), if \({\frac{a_1}{a_2}}\ne{\frac{b_1}{b_2}}\), then the equations will represent:

(a) coincident lines

(b) parallel lines

(c) intersecting lines

(d) none

The pair of equations 5x – 15y = 8 and \(3x-9y=\frac{24}{5}\) has:  

(a) one solution

(b) two solutions

(c) infinitely many solutions

(d) no solution

A pair of linear equations which has a unique solution x = 2, y = –3 is:

(a) x + y = –1, 2x – 3y = –5

(b) 2x + 5y = –11, 4x + 10y = –22

(c) 2x – y = 1, 3x + 2y = 0

(d) x – 4y – 14 = 0, 5x – y – 13 = 0

The value of k for which the system: 

4x + 2y = 3, (k – 1)x – 6y = 9

has no unique solution is:

(a) –13

(b) 9

(c) –11

(d) 13

The sum of the digits of a two-digit number is 9. If 27 is added to it, digits of the number get reversed. The number is:

(a) 63

(b) 72

(c) 81

(d) 36 

Graphically, the pair of equations 6x – 3y + 10 = 0 and 2x – y + 9 = 0  represents two lines which are:

(a) intersecting at exactly one point       

(b) intersecting at exactly two points  

(c) coincident

(d) parallel

For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16, represent coincident lines?

(a) \(1\over 2\)

(b) \(-1\over 2\)

(c) 2

(d) − 2